User blog:3primetime3/The Question of the Day - 04/20/2014
Hey guys! I'm seeing a lot of new users! That's so great! New users: even if an answer is already seen in the comments section, still write your answer. The answers not written by me still might not be right. For newcomers who are seeing this blog post for the first time, please read the rules to get started! Achievements earned during the last question: 1 X1 Quick Thinker (founded by Minipop56) The Question of the Day – 50 points Please show your work! Three mutually tangent spheres each with radius r = 5 sit on a horizontal plane. A triangular pyramid has a base that is an equilateral triangle with side length 6, has three congruent isosceles triangles for vertical faces, and has height h = 12. The base of the pyramid is parallel to the plane, and the vertex of the pyramid is pointing downward so that it is between the base and the plane. Each of the three vertical faces of the pyramid is tangent to one of the spheres at a point on the triangular face along its altitude from the vertex of the pyramid to the side of length 6. The distance that these points of tangency are from the base of the pyramid is m/n, where m and n are relatively prime positive integers. Find m + n. Lucky Prime Hint: Contains three digits! Previous Solution THE QUADRATIC FORMULA!!! Scoreboards 1. Blueeighthnote: 13555 points (2 achvmt pkgs) - One more to get the next lucky prime badge! 2. Minipop56: 1010 points - One more to get the next lucky prime badge! 3. TimBluesWin: 755 points (1 achvmt pkg) 4. Imamadmad: 745 points (1 achvmt pkg) 5. Julianthewiki: 525 points (1 achvmt pkg) - RETIRED 6. Wikia Contributor 69.235...: 230 points (1 achvmt pkg) 7. Lefty7788: 300 points - One more to get the next lucky prime badge! 8. Supermario3459: 145 points (1 achvmt pkg) 9. Dalek-James: 120 points 10. ZombieBird4000: 50 points (1 achvmt pkg) 11. Wildoneshelper: 40 points (1 achvmt pkg) 12. Emmaelise401: 50 points 13. CalzoneManiac: 30 points 14. 21qmcgagin: 20 points 15. Googleaarex: 10 points Achievements Skillz Badges! Usually awarded for having skills to solving hard questions, etc. 1. Quick Thinker! (+10 points) - Awarded for posting an answer before I write "Please leave your answers here." FIRST FOUNDED BY BLUEEIGHTHNOTE 2. RARE: Leaderboards Expert! (+300 points) - Awarded for being 1st place on the leaderboards for 30+ days. FIRST FOUNDED BY BLUEEIGHTHNOTE 3. RARE: More than a Millenium! (+100 points) - Awarded for being first in the leaderboards and scoring more than 1000 points from the runner-up. FIRST FOUNDED BY BLUEEIGHTHNOTE 4. Questions in a question (+20 points)? Awarded for finding three ambiguities in a single question. EARNED BY IMAMADMAD Earth Badges Most rare ones are found here. 1. RARE: Top Ten (+30 points) - Awarded for being the first top 10 people ONLY to participate on the question of the day! EARNED BY THE FIRST 10 PARTICIPATING PEOPLE 2. RARE: Cyclone Centurion! (+250 points) - Awarded for scoring at least 10000 points in the QOTD system! FIRST FOUNDED BY BLUEEIGHTHNOTE. Sun Badges All epic ones are found here. 1. EPIC: Lucky Primer (+100 points): Congratulations! You have guessed the lucky prime correctly. Get the Lucky Prime two more times to earn the next achievement! FIRST FOUNDED BY JULIANTHEWIKI. 2. EPIC: Very Lucky Primer (+200 points): Congratulations! You have guessed the lucky prime correctly two more times. Get the Lucky Prime three more times to earn the next achievement! FIRST FOUNDED BY MINIPOP56 AND BLUEEIGHTHNOTE. Galaxy Badges Mysterious badges from a far-out universe. Each one found here is worth 10000+ points and/or 5+ achievement packages. 1. MYSTERY: ATLAS (+10000 points) - ??? FIRST FOUNDED BY BLUEEIGHTHNOTE. Uniqueness Badges Unique things one can do in the answers section. ONLY ONE PERSON CAN EARN EACH BADGE. 1. Analyzer! (+10 points) - Awarded for drawing a diagram. FOUNDED BY IMAMADMAD 2. Inspiration! (+5 points) - A question was dedicated to you! FOUNDED BY BLUEEIGHTHNOTE Trustworthiness Badges Awarded by how much I trust someone on this wiki. Please do not ask me about these badges. 1. Reliability (+100 points) - Trusted to write a question of a day. FIRST FOUNDED BY BLUEEIGHTHNOTE, AND IMAMADMAD 2. Scoreboard Tinkerer (+100 points) - Trusted to change the scoreboards. FIRST FOUNDED BY BLUEEIGHTHNOTE AND JULIANTHEWIKI 3. Prime Staff (+100 points) - Become a chat moderator, rollbacker, sysop, or bureaucrat on this wikia! FIRST FOUNDED BY BLUEEIGHTHNOTE, JULIANTHEWIKI, TIMBLUESWIN, IMAMADMAD, SUPERMARIO3459, MINIPOP56, AND DALEK-JAMES Duration Badges Yes! YOU KNOW IT! PARTICIPATION EVERY DAY! 1. 4-Leaf Clover! (+100 points) - Awarded for participating on the Question of the Day everyday during the month of March! FIRST FOUNDED BY MINIPOP56. Category:Blog posts